To estimate the solution to the system of the equations \(y = 2x + 3\) and \(y = 12x + 6\) based on the given options, we can find the intersection of the two lines, which represents the solution to the system.
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Set the equations equal to each other to find the intersection point:
\[ 2x + 3 = 12x + 6 \]
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Rearranging the equation:
\[ 3 - 6 = 12x - 2x \] \[ -3 = 10x \] \[ x = -\frac{3}{10} \]
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Substituting this \(x\) value back into one of the original equations to find \(y\). We'll use the first equation \(y = 2x + 3\):
\[ y = 2\left(-\frac{3}{10}\right) + 3 = -\frac{6}{10} + 3 = -\frac{6}{10} + \frac{30}{10} = \frac{24}{10} = \frac{12}{5} = 2.4 \]
Thus, the intersection point, or the solution to this system of equations, is approximately \((-0.3, 2.4)\).
- Now comparing this with the provided options:
- (7, 2)
- (2,−7)
- (−2, 7)
- (2, 7)
None of the provided options match the intersection point \((-0.3, 2.4)\). However, considering the context of your question and the approximate nature of solutions that could be based on a graph, (2, 7) might be the closest estimate depending on any visual interpretation of the intersection.
Thus, the best choice here would be (2, 7), understanding that it is an estimation due to the lack of exact intersections among the choices.